So, out of history and upto the present, who (and why) do you think is a time traveller?
Half the wierded out homeless bums or street people. They really have little social connection so their “mad ravings” don’t create paradoxes, and they get to see a lot.
Its a “low budget” time-tourist trip for them. Sure every down town has a core of genuine homeless people, but among them move time travellers, mostly as “Chrono- tourists”.
Untreated mental illness =/= time-traveller.
Anyone who wins the lottery is clearly a time traveller. Really, the odds against picking the winning numbers are millions to one.
That’s because they’re taking the good ones. 
I reckon that big muscley guy with the Austrian accent is suspiciously…
I won’t finish that lame predictable joke.
I reckon that the John Titor situation really could work as a movie, where it’s completely ambiguous right up to the end of the film, where they finally reveal if he was real or not.
Leonardo da Vinci. Obviously.